What is the thermodynamic definition of entropy represented by?

The thermodynamic definition of entropy is represented by the differential form dS = dq_rev / T. This expression reflects how entropy, S, changes under reversible processes. In this equation, dS is the change in entropy, dq_rev is the reversible heat exchange at constant temperature, and T is the absolute temperature at which this exchange occurs.

This definition highlights the relationship between heat transfer and entropy. For a reversible process, the amount of heat added to the system is divided by the temperature, which quantifies the contribution of heat to the entropy change. As this equation is derived from the second law of thermodynamics, it emphasizes that entropy increases in a system as it undergoes reversible heat exchanges.

While the other options reference aspects of entropy, they do not capture the thermodynamic definition in the same comprehensive way. For example, ΔS = q/T implies a finite change in entropy for a specific process but does not specify the necessity of reversibility, which is key to the definition. Similarly, ΔS = dq / T lacks the qualifier of reversible heat exchange, and S = k ln(q) describes a statistical view of entropy rather than its thermodynamic basis.